Can I update a Make Human model in Blender without losing my animation?
I'd go with option 3, especially if your deadline is tomorrow.  Especially if it's just a matter of re-topoligizing, and then re-weightpainting just a bit.

If you want to learn from this, I suggest try having a master-slave style rig.  That means you have one set of bones you animate directly, and those bones in turn constrain a bunch of 'slave' bones that only deform the mesh.  That way if you want to re-import your model later on, you can simply re-constrain those 'fresh' new bones to your older animation rig.  

You can even have two separate armatures, one for deforming, one for animating to make the re-constraining process clear to yourself.  Although I've found this method a tad obscure, and not considered canonical Blender rigging.